Using the distributive property of multiplication over
addition, we can factor as in x2 + xy = x1x + y2. Use
the distributive property and other multiplication properties
to factor each of the following:
47.99 + 47
(x+1)Y +(X+1)
x^2y+z^x3
1. 47*99 + 47.
47 is common to both terms. Therefore we factor out 47:
47(99+1).
2. (x+1)y + (x+1)1.
x+1 is common to both terms. So we factor out x+1.
(x+1)(y+1).
3. No common terms.
post.
To factor the given expressions, we will use the distributive property and other multiplication properties.
1) 47.99 + 47:
There is no common factor that can be factored out in this expression, so it remains as it is.
2) (x+1)Y + (X+1):
Using the distributive property, we can expand the multiplication:
(x+1)Y + (X+1) = xY + Y + x + 1
Now, we can rearrange the terms:
xY + Y + x + 1 = xY + x + Y + 1
3) x^2y + z^x3:
This expression is a bit unclear, so I'll provide two interpretations:
a) If the expression is x^2y + z^(x*3), meaning z raised to the power of (x multiplied by 3), then we can rewrite it as:
x^2y + z^(x*3) = x^2y + z^(3x)
b) If the expression is x^2y + z^(x^3), meaning z raised to the power of (x cubed), then we can write it as:
x^2y + z^(x^3)
In both cases, no further factoring can be done using the given information.
To factor each of the given expressions using the distributive property and other multiplication properties, let's go through them one by one:
1. 47.99 + 47:
The expression 47.99 + 47 is already in its simplest form and cannot be factored further. The distributive property does not apply here since we are not dealing with multiplication.
2. (x+1)y + (x+1):
To factor the expression (x+1)y + (x+1), we can apply the distributive property. Notice that both terms in parentheses have the common factor (x+1). We can factor it out: (x+1)(y+1).
3. x^2y + z^x3:
This expression is a bit more complex. We can factor it by using the distributive property and simplifying further.
First, let's look at x^2y. Since x and y are multiplied, we can factor this term as (xy).
Now, let's focus on z^x3. This expression involves an exponent, which means we need to use the multiplication property for exponents. When multiplying exponents with the same base, we add the exponents. So we can rewrite z^x3 as z^(3+x).
Putting it all together, the factored expression is (xy) + z^(3+x).
Remember, factoring is the process of representing an expression as a product of its factors. By applying the distributive property and using the appropriate multiplication properties, we can simplify expressions and find their factored forms.